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What is the point of intersection of the curves $y=3^{x-1}\ln x$ and $y=x^x-1$?

By hit and trial, I got the intersection point as $(1,0)$. Is there any other way I could find the intersection?

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    Well I dont think there is any other way than trial . To show that there are no more solutions, you can use calculus. – King Tut Apr 06 '18 at 13:15

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